Proveden

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HEAT PROCESSES
Thermodynamicsprocesses and cycles
Thermodynamics fundamentals. State variables,
Gibbs phase rule, state equations, internal
energy, enthalpy, entropy. First law and the
second law of thermodynamics. Phase changes and
phase diagrams. Ts and hs diagrams (example Ts
diagrams for air). Thermodynamic cycles Carnot,
Clausius Rankine, Ericson, Stirling,
thermoacoustics.
Rudolf Žitný, Ústav procesní a zpracovatelské
techniky CVUT FS 2010
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FUNDAMENTALS of THERMODYNAMICS
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Estes
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BASIC NOTIONS
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Subsystem flame zone opened

• SYSTEM
• Insulated- without mass or energy transfer
• Closed (without mass transfer)
• Opened (mass and heat transport through
  boundary).
• Thermal units operating in continuous mode (heat
  exchangers, evaporators, driers, tubular
  reactors, burners) are opened systems
• Thermal units operating in a batch mode (some
  chemical reactors) are closed systems

Subsystem candlewick opened
Subsystem candle opened with moving boundary
Subsystem stand closed
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StaTE VARIABLES
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state of system is characterized by

• THERMODYNAMIC STATE VARIABLES related with
  directly measurable mechanical properties
• T K, p PaJ/m3, v m3/kg (temperature,
  pressure, specific volume)

• Thermodynamické state variables related to energy
  (could be derived from T,p,v)
• u J/kg internal energy
• s J/kg/K specific entropy
• h J/kg enthalpy
• g J/kg gibbs energy
• e J/kg exergy

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Gibbs phase rule
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Not all state variables are independent. Number
of independent variables (DOF, Degree Of Freedom)
is given by Gibbs rule
NDOF Ncomponents Nphases 2

• 1 component, 1 phase (e.g.gaseous oxygen)
  NDOF2 . In this case only two state variables
  can be selected arbitrarily, e.g. p,v, or p,T or
  v,T.
• 1 component, 2 phases (e.g. equilibrium mixture
  of water and steam at the state of
  evaporation/condensation). In this case only one
  state variable can be selected, e.g. pressure
  (boiling point temperature is determined by p)

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State EquATIONS p-v-T
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Van der Waals equation isotherms
Critical point, solution of these two equations
give a,b parameters as a function of critical
temperature and critical pressure
Above critical temperature Tc the substance
exists only as a gas (liquefaction is not
possible even at infinitely great pressure)
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PvRT tutorial Baloon
Example Calculate load capacity of a baloon
filled by hot air. D20m, T600C, Te200C, p105
Pa.
M29 (air)
D
m
599 kg
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Internal energy u J/kg
u-all forms of energy of matter inside the system
(J/kg), invariant with respect to coordinate
system (potential energy of height /gh/ and
kinetic energy of motion of the whole system
/½w2/ are not included in the internal energy).
Internal energy is determined by structure,
composition and momentum of all components, i.e.
all atoms and molecules.

• Nuclear energy (nucleus) 1017J/kg
• Chemical energy of ionic/covalent bonds in
  molecule 107 J/kg
• Intermolecular VdW forces (phase changes)
  106 J/kg
• Thermal energy (kinetic energy of molecules)
  104 J/kg

Only the following item (thermal energy) is often
included into the internal energy concept
(sometimes distinguished as the sensible internal
energy)
It follows from energy balances that the change
of internal energy of a closed system at a
constant volume equals amount of heat delivered
to the system du dq (heat added at isochoric
change)
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Enthalpy h J/kg
hupv enthalpy is always greater than the
internal energy. The added term pv (pressure
multiplied by specific volume) simplifies energy
balancing of continuous systems. The pv term
automatically takes into account mechanical work
(energy) necessary to push/pull the inlet/outlet
material streams to/from the balanced system.
It follows from energy balances that the change
of enthalpy of a closed system at a constant
pressure equals amount of heat delivered to the
system dh dq (heat added at isobaric change)
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Entropy s J/kg/K
Thermodynamic definition of entropy s by Clausius
where ds is the specific entropy change of
system corresponding to the heat dq J/kg added
in a reversible way at temperature T K.
Boltzmanns statistical approach Entropy
represents probability of a macroscopic state
(macrostate is temperature, concentration,).
This probability is proportional to the number of
microstates corresponding to a macrostate (number
of possible configurations, e.g. distribution of
molecules to different energy levels, for given
temperature).
It follows from energy balances that the change
of entropy of a closed system at a constant
temperature equals amount of heat delivered to
the system / T Tds dq (heat added at an
isothermal and reversible change)
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Laws of thermodynamics
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Modigliani
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Laws of thermodynamics
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First law of thermodynamics (conservation of
energy)
dw work done by system
dq heat added to system
expansion work (p.dV) in case of compressible
fluids, surface work (surface tension x increase
of surface), shear stresses x displacement, but
also electrical work (intensity of electric field
x current). Later on we shall use only the p.dV
mechanical expansion work.
dq du dw
Second law of thermodynamics (entropy of closed
insulated system increases)
dq heat added to system is Tds only in the case
of reversible process
Tds ? dq
Combined first and second law of thermodynamics
Tds dupdv
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Energies and Temperature
The temperature increase increases thermal energy
(kinetic energy of molecules). For constant
volume (fixed volume of system) internal energy
change is proportional to the change of
thermodynamic temperature (Kelvins) du cv
dT where cv is specific heat at constant
volume For constant pressure (e.g. atmospheric
pressure) the enthalpy change is also
proportional to the thermodynamic temperature
dh cp dT where cp is specific heat at
constant pressure. Specific heat at a constant
pressure is always greater than the specific heat
at a constant volume (it is always necessary to
supply more heat to increase temperature at
constant pressure, because part of the delivered
energy is converted to the volume increase,
therefore to the mechanical work). Only for
incompressible materials it holds cpcv.
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u(T,v) internal energy change
How to evaluate internal energy change? Previous
relationship ducvdT holds only at a constant
volume. However, according to Gibbs rule the du
should depend upon a pair of state variables (for
a one phase system). So how to calculate du as
soon as not only the temperature (dT) but also
the specific volume (dv) are changing? Solution
is based upon the 1st law of thermodynamic (for
reversible changes) where du is expressed in
terms dT and dv (this is what we need),
coefficient at dT is known (cv), however entropy
appears at the dv term. It is not possible to
measure entropy directly (so how to evaluate
ds/dv?), but it is possible to use Maxwell
relationships, stating for example that Instead
of exact derivation I can give you only an idea
based upon dimensional analysis dimension of s/v
is Pa/K and this is just the dimension of p/T!
So there is the final result
cv
ds
This term is zero for ideal gas (pvRT)
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h(T,p) enthalpy changes
The same approach can be applied for the enthalpy
change. So far we can calculate only the enthalpy
change at constant pressure (dhcpdT). Using
definition hupv and the first law of
thermodynamics And the same problem how to
express the entropy term ds/dp by something that
is directly measurable. Dimensional analysis s/p
has dimension J/(kg.K.Pa)m3/(kg.K) and this is
dimension of v/T. Corresponding Maxwells
relationship is After substuting we arrive to
the final expression for enthalpy
change Negative sign in the Maxwell equation
is probably confusing, and cannot be derived from
dimensional analysis. Correct derivation is
presented in the following slide.
cp
Tds
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s(T,v) s(T,p) entropy changes
Changes of entropy follow from previous equations
for internal energy and enthalpy
changes Special case for IDEAL GAS (pvRmT,
where Rm is individual gas constant) Please
notice the difference between universal and
individual gas constant. And the difference
between molar and specific volume.
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u,h,s finite changes (without phase changes or
reactions)
Previous equations describe only differential
changes. Finite changes must be calculated by
their integration. This integration can be
carried out analytically for constant values of
heat capacities cp, cp and for state equation of
ideal gas
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u,h,s finite changes during phase changes
During phase changes (evaporation, condensation,
melting,) both temperature T and pressure p
remain constant. Only specific volume varies and
the enthalpy/entropy changes depend upon only one
state variable (for example temperature). These
functions are tabulated (e.g. ?h-enthalpy of
evaporation) as a function of temperature (see
table for evaporation of water), or approximated
by correlation
T0C pPa ?hkJ/kg
0 593 2538
50 12335 2404
100 101384 2255
200 1559120 1898
300 8498611 1373
Tc647 K, T1373 K, r2255 kJ/kg, n0.38 for water
Pressure corresponding to the phase change
temperature is calculated from Antoines equation
C-46 K, B3816.44, A23.1964 for water
Entropy change is calculated directly from the
enthalpy change
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h,s during phase changes (phase diagram p-T)
Melting ?hSLgt0, ?sSLgt0,,
Evaporation ?hLGgt0, ?sLGgt0,
Sublimation ?hSGgt0, ?sSGgt0,
Phase transition lines in the p-T diagram are
described by the Clausius Clapeyron equation
?hLG
Specific volume changes, e.g. vG-vL
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SUMMARY
State equation p,v,T. Ideal gas pVnRT (n-number
of moles, R8.314 J/mol.K) First law of
thermodynamics (and entropy change) Internal
energy increment (ducv.dT for constant volume
dv0) Enthalpy increment (dhcp.dT for
constant pressure dp0)

These terms are zero for ideal gas (pvRT)
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Check units
It is always useful to check units all terms in
equations must have the same dimension. Examples
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Important values
cvcp ice 2 kJ/(kg.K) cvcp water 4.2
kJ/(kg.K) cp steam 2 kJ/(kg.K) cp air
1 kJ/(kg.K) ?henthalpyof
evaporation water 2.2 MJ/kg R 8.314
kJ/(kmol.K) Rm water 8.314/18 0.462 kJ/(kg.K)
Example Density of steam at 200 oC and pressure
1 bar.
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THERMODYNAMICDIAGRAMS
Delvaux
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DIAGRAM T-s
isobars
Critical point
isochors
Left curve-liquid
Right curve-saturated steam
Implementation of previous equations in the T-s
diagram with isobars and isochoric lines.
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DIAGRAM h-s
Critical point
Left curve liquid
Right curve saturated steam
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Thermodynamic processes

• Basic processes in thermal apparatuses are
• Isobaric dp0 (heat exchangers, ducts, continuous
  reactors)
• Isoentropic ds0 (adiabatic-thermally insulated
  apparatus, ideal flow without friction, enthalpy
  changes are fully converted to mechanical energy
  compressors, turbines, nozzles)
• Isoenthalpic dh0 (also adiabatic without heat
  exchange with environment, but no mechanical work
  is done and pressure energy is dissipated to
  heat throttling in reduction valves)

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Thermodynamic processes
STEAM expansion in a turbine the enthalpy
decrease is transformed to kinetic energy,
entropy is almost constant (slight increase
corresponds to friction)
h
T
Expansion of saturated steam in a nozzle the same
as turbine (purpose convert enthalpy to kinetic
energy of jet)
s
s
Steam compression power consumption of compressor
is given by enthalpy increase
Throttling of steam in a valve or in a porous
plug. Enthalpy remains constant while pressure
decreases. See next lecture Joule Thomson effect.
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Thermodynamic processes
Superheater of steam. Pressure only slightly
decreases (friction), temperature and enthalpy
increases. Heat delivered to steam is the
enthalpy increase (isobaric process). The heat is
also hatched area in the Ts diagram (integral of
dqTds).
Boiler (evaporation at the boiling point
temperatrure) constant temperature, pressure.
Density decreases, enthalpy and entropy
increases. Hatched area is the enthalpy of
evaporation.
Mixing of condensate and superheated steam
purpose of mixing is to generate a saturated
steam from a superheated steam. Resulting state
is determined by masses of condensate and steam
(lever rule).
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Thermodynamic cycles
Periodically repeating processes with working
fluid (water, hydrocarbons, CO2,) when heat is
supplied to the fluid in the first phase of the
process followed by the second phase of heat
removal (final state of the working medium is the
same as the initial one, therefore the cycle can
be repeated infinitely many times). Because more
heat is supplied in the first phase than in the
second phase, the difference is the mechanical
work done by the working medium in a turbine
(e.g.). It follows from the first law of
thermodynamics.
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Thermodynamic cycles
Carnot cycle Mechanical work
3
Clausius Rankine cycle Cycle makes use phase
changes. Example POWERPLANTS. 1-2 feed pump
2-3 boiler and heat
exchangers 3-4 turbine
and generator 4-5
condenser
T
2
4
1
s
Ericsson cycle John Ericsson designed (200 years
ago) several interesting cycles working with only
gaseous phase. Reversed cycle (counterclock
orientation) is applied in air conditioning see
Brayton cycle shown in diagrams.
3
2
1
4
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Stirling machine
Stirling ENGINE
Stirling cycle Gas cycle having thermodynamic
efficiency of Carnot cycle. Casn be used as
engine or heat pump (Stirling machnines
fy.Philips are used in cryogenics). Efficiency
can be increased by heat regenerator (usually a
porous insert in the displacement channel capable
to absorb heat from the flowing gas).

1. Compression and transport of cool gas to heater
2. Expansion of hot gas
3. Displacement of gas from hot to cool section
4. Compression (phase 1)

ß-Stirling
Stirling HEAT PUMP
?-Stirling with regenerator
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Thermoacoustical engine
Thermoacoustic analogy of Stirling
engine Very simple design can be seen on
Internet video engines. Cylinder can be a glass
test tube with inserted porous layer (stack).
Besides toys there exist applications with rather
great power driven by solar energy or there exist
equipments for cryogenics liquefaction of
natural gas.
Standing waves mutually shifted pressure and
velocity waves (90o)
Wave equation for pressure, velocity. C is speed
of sound
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Thermoacoustics
Phenomena and principles of thermoacoustics are
more than hundred years old.
Singing Rijke tube Rijke P.L. Annalen der Physik
107 (1859), 339
Sondhauss tube Sondhauss C. Annalen der Physik 79
(1850), 1
Taconis oscillations Taconis K.W. Physica 15
(1949) 738
Thin tube
Thin tube inserted into a cryogenic liquid
Heated bulb
Liquid helium

• Lord Rayleigh authorLord Rayleigh titleThe
  explanation of certain acoustical phenomena
  journalNature (London) year1878 volume18
  pages319321 formulated principles as follows
  
• thermoacoustic oscillations are generated as soon
  as
• Heat is supplied to the gas at a place of
  greatest condensation (maximum density)
• Heat is removed at a place of maximum rarefaction
  (minimum pressure)

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Magnetic refrigeration
Application of magnetic field upon ferromagnetic
material causes orientation of magnetic spin of
molecules therefore decreases the magnetic
entropy. Total entropy (sum of the magnetisation
entropy and the lattice entropy, thermal
vibration of molecules in a crystal lattice)
remains constant assuming a thermally insulated
(adiabatic) systém. Therefore the magnetic
entropy decrease must be compensated by the
thermal entropy (and temperature) increase. The
first law of thermodynamic can be formulated in
terms of internal energy as
(?o magnetic permeability of vacuum, H intensity
of magnetic field T,? specific magnetisation)
For constant volume the relationship between
entropy, temperature and H is
This equation enables to construct the T-s
diagrams and demonstrate thermodynamic cycles of
refrigeration.
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Laser cooling
Lasers illuminating crystals achieve extremely
low cryogenic temperatures of 10-9 K.
Ruan X.L. et al. Entropy and efficiency in laser
cooling solids. Physical Review B, 75 (2007),
214304
A phonon is a quantum of collective excitation in
a periodic, elastic arrangement of atoms or
molecules in condensed matter.
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EXAM
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Thermodynamics
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What is important (at least for exam)
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Gibbs phase rule State equations Van der Waals
and critical parameters
NDOF Ncomponents Nphases 2
First law of thermodynamics
Tds dupdv
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What is important (at least for exam)
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Carnot
Clausius Rankine
Ericsson
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What is important (at least for exam)
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regenerator
T
STIRLING
displacing piston
Thermoacoustic standing wave
compression/expansion wave stack
s
Thermoacoustic travelling wave
regenerator
AMR Active Magnetic Refrigerator